I'm working on a problem that looks at growth models and I'm trying to show that the equation,
$\frac{dN}{dt}$ = $aN^{\gamma}$ - $bN^{\gamma}$($\frac{N^{\gamma -1} - 1}{1 - \gamma}$)
is equivalent to the equation
$\frac{dN}{dt}$ = $-bNlog(\frac{N}{K})$
for the limit $\gamma \to 1^{-}$
The first equation is a rewritten version of the Bertalanffy equation and the second is the Gompertz equation. The Gompertz equation would be a special case of the Berttananffy equation. We would want to find $K$ in terms of $a$ and $b$ aswell.
Any help would be appreciated thank you.